Hölder Continuity for Fully Fractional Parabolic Equations with Space-time Nonlocal Operators
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917692474130432 |
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| author | Ma, Lingwei Xiong, Qi Zhang, Zhenqiu |
| author_facet | Ma, Lingwei Xiong, Qi Zhang, Zhenqiu |
| contents | We study the local Hölder regularity of weak solutions to the fully fractional parabolic equations involving spatial fractional diffusion and fractional time derivatives of the Marchaud type. It is worth noting that we do not impose boundedness assumptions on the weak solutions and nonhomogeneous terms. Within the space-time nonlocal framework, it is crucial to consider both space-dependent nonlocal tail terms and the first introduced time-dependent nonlocal tail term. By adapting a nonlocal variant of the parabolic De Giorgi iterative technique, we initially establish a priori local boundedness with tail terms for weak solutions and then prove the local Hölder continuity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08795 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hölder Continuity for Fully Fractional Parabolic Equations with Space-time Nonlocal Operators Ma, Lingwei Xiong, Qi Zhang, Zhenqiu Analysis of PDEs We study the local Hölder regularity of weak solutions to the fully fractional parabolic equations involving spatial fractional diffusion and fractional time derivatives of the Marchaud type. It is worth noting that we do not impose boundedness assumptions on the weak solutions and nonhomogeneous terms. Within the space-time nonlocal framework, it is crucial to consider both space-dependent nonlocal tail terms and the first introduced time-dependent nonlocal tail term. By adapting a nonlocal variant of the parabolic De Giorgi iterative technique, we initially establish a priori local boundedness with tail terms for weak solutions and then prove the local Hölder continuity. |
| title | Hölder Continuity for Fully Fractional Parabolic Equations with Space-time Nonlocal Operators |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.08795 |